How do I determine whether or not a system will correlate to a fractal?
So I am investigating the one dimensional Abelian Sandpile for an undergraduate research project. I am primarily investigating whether or not, there is a connection between this model and the Farey Sequence.
I've been flipping through a few papers, most far above my level, but I came across a paper "Toppling distributions in one-dimensional Abelian sandpiles," by P. Ruelle and S. Sen which states that the one-dimensional case does not exhibit criticality. If someone could explain what this means, I would be most grateful.
Finally, I wanted to read the paper by Levine, Pegden, and Smart which correlates the two-dimensional case of the Abelian Sandpile to Apollonian Circles, for further insight on the problem. However, it requires a background in PDEs. which I am currently lacking. Does anyone know if Evans' PDE book discusses this?
analysis pde fractals
asked Dec 2 '18 at 4:21
Josabanks
936
add a comment |
So I am investigating the one dimensional Abelian Sandpile for an undergraduate research project. I am primarily investigating whether or not, there is a connection between this model and the Farey Sequence.
I've been flipping through a few papers, most far above my level, but I came across a paper "Toppling distributions in one-dimensional Abelian sandpiles," by P. Ruelle and S. Sen which states that the one-dimensional case does not exhibit criticality. If someone could explain what this means, I would be most grateful.
Finally, I wanted to read the paper by Levine, Pegden, and Smart which correlates the two-dimensional case of the Abelian Sandpile to Apollonian Circles, for further insight on the problem. However, it requires a background in PDEs. which I am currently lacking. Does anyone know if Evans' PDE book discusses this?
analysis pde fractals
asked Dec 2 '18 at 4:21
Josabanks
936
add a comment |
So I am investigating the one dimensional Abelian Sandpile for an undergraduate research project. I am primarily investigating whether or not, there is a connection between this model and the Farey Sequence.
I've been flipping through a few papers, most far above my level, but I came across a paper "Toppling distributions in one-dimensional Abelian sandpiles," by P. Ruelle and S. Sen which states that the one-dimensional case does not exhibit criticality. If someone could explain what this means, I would be most grateful.
Finally, I wanted to read the paper by Levine, Pegden, and Smart which correlates the two-dimensional case of the Abelian Sandpile to Apollonian Circles, for further insight on the problem. However, it requires a background in PDEs. which I am currently lacking. Does anyone know if Evans' PDE book discusses this?
analysis pde fractals
asked Dec 2 '18 at 4:21
Josabanks
936
So I am investigating the one dimensional Abelian Sandpile for an undergraduate research project. I am primarily investigating whether or not, there is a connection between this model and the Farey Sequence.
I've been flipping through a few papers, most far above my level, but I came across a paper "Toppling distributions in one-dimensional Abelian sandpiles," by P. Ruelle and S. Sen which states that the one-dimensional case does not exhibit criticality. If someone could explain what this means, I would be most grateful.
Finally, I wanted to read the paper by Levine, Pegden, and Smart which correlates the two-dimensional case of the Abelian Sandpile to Apollonian Circles, for further insight on the problem. However, it requires a background in PDEs. which I am currently lacking. Does anyone know if Evans' PDE book discusses this?
analysis pde fractals
analysis pde fractals
asked Dec 2 '18 at 4:21
Josabanks
936
asked Dec 2 '18 at 4:21
Josabanks
936
asked Dec 2 '18 at 4:21
Josabanks
936
asked Dec 2 '18 at 4:21
Josabanks
936
asked Dec 2 '18 at 4:21
Josabanks
936
936
add a comment |
add a comment |
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